Homework Help: Proof sin(10) is irrational.

1. Oct 15, 2012

SrEstroncio

1. The problem statement, all variables and given/known data
Prove $\sin{10}$, in degrees, is irrational.

2. Relevant equations
None, got the problem as is.

3. The attempt at a solution
Im kinda lost.

2. Oct 15, 2012

Zondrina

Okay, are you familiar with proof by contradiction?

Start by contradicting the statement :

Suppose that sin(10) is irrational.

3. Oct 15, 2012

Dick

Let x=sin(10). You'll want to find a polynomial x satisfies and show it has no rational root. Hint: sin(30)=1/2=sin(10+10+10).

4. Oct 15, 2012

SrEstroncio

I should suppose sin(10) is rational, if i am to contradict the statement, shouldnt i?

5. Oct 15, 2012

Staff: Mentor

yes and that means that sin(10) can be represented by the ratio of two integers a and b sin(10) = a/b

next step...

6. Oct 15, 2012

Dick

Zondrina's hint contains nothing of any real substance to start solving the problem. Mine does. I suggest you start trying it.